The first application of particle number projection in the fragments was done
in [1]}. The formalism was presented in more details in
[2]} and was applied for the first time in the calculation of
primary fission fragment charge, mass and isotopic distributions in
[3]}. This technique has several advantages. First, it can be
applied to phenomenological models based, e.g., on the macroscopic-microscopic
model. The only ingredient needed is a set of single-particle levels associated
with each configuration. Second, the method guarantees that the fragments will
have an integer number of particles – as nature tells us. Finally, by
substituting at each scission point a single pair of average numbers
\((\bar{Z}_{\rm R}, \bar{N}_{\rm R})\)  by a two-dimensional probability
distribution function \(\mathbb {P}(Z_{\rm R},N_{\rm R}| Z,N,\mathbf {q})\) , which
is equal to \(\mathbb {P}(Z_{\rm R}| Z, \mathbf {q}) \times \mathbb {P}(N_{\rm R}| N, \mathbf {q})\)  if calculations do not account for isospin
mixing, the method produces much more realistic estimates of which fragments
are populated. We will show later how this technique can be applied to compute
isotopic yields \(Y(Z,A)\)  of neutron-induced fission reactions.
